Testing dominance of biometric functions

The hazard rate (HR) and mean residual lifetime are two of the most practical and best-known functions in biometry, reliability, statistics and life testing. Recently, the reversed HR function is found to have interesting properties useful in additional areas such as censored data and forensic science. For these three biometric functions, we propose testing methods that they take on a known functional form against that they dominate or are dominated by this known form. This goodness-of-fit-type testing is wider in applications and more interesting than the long-standing testing procedures for exponentiality against the monotonicity of these functions or even the change point problems. This is so since we can test against any choice of the survival distribution and not just exponentiality. For this general testing, we present easy to implement tests and generalize them into classes of statistics that could lead to more powerful and efficient testing.     

Testing hypotheses for the growth curve model when the data are incomplete

Kleinbaum (1973) developed a generalized growth curve model for analyzing incomplete longitudinal data. In this paper the small sample properties of several related test statistics are investigated via Monte Carlo techniques. The covariance matrix is estimated by each of three non-iterative methods. The null and non-null distributions of these test statistics are examined.     

统计显著性:一个被误读的P值——基于美国统计学会的声明

美国统计学会"关于统计显著性与P值"的官方声明发布之后,再次引发国内外研究学者对P值的广泛关注。在介绍国内统计教材中假设检验的基本内容和步骤的基础上,以"硬币投掷"与"背影识人"为例直观性解释P值、统计显著性与统计功效等相关概念,并引用心理学统计经典调查案例分析P值被误读的原因。同时,基于美国统计学会的声明,给出正确使用P值的建议。     

Confidence distributions applied to propagating uncertainty to inference based on estimating the local false discovery rate: A fiducial continuum from confidence sets to empirical Bayes set estimates as the number of comparisons increases

Empirical Bayes estimates of the local false discovery rate can reflect uncertainty about the estimated prior by supplementing their Bayesian posterior probabilities with confidence levels as posterior probabilities. This use of coherent fiducial inference with hierarchical models generates set estimators that propagate uncertainty to varying degrees. Some of the set estimates approach estimates from plug-in empirical Bayes methods for high numbers of comparisons and can come close to the usual confidence sets given a sufficiently low number of comparisons.     

On Pitman's measure of closeness of k-records

Pitman closeness of both the upper and lower k-record statistics to the population quantiles of a location–scale family of distributions is studied. For the population median, the Pitman-closest k-record is also determined. In the case of symmetric distributions, the Pitman closeness probabilities of k-record statistics are shown to be distribution-free, and explicit expressions are also derived for these probabilities. Exact expressions are derived for the required probabilities for uniform and exponential distributions. Numerical results are given for these families and also the Pitman-closest k-record is determined.     

On tests of symmetry,marginal homogeneity and quasi-symmetry in two-way contingency tables based on minimum φ-divergence estimator with constraints

The restricted minimum φ-divergence estimator, [Pardo, J.A., Pardo, L. and Zografos, K., 2002, Minimum φ-divergence estimators with constraints in multinomial populations. Journal of Statistical Planning and Inference, 104, 221–237], is employed to obtain estimates of the cell frequencies of an I×I contingency table under hypotheses of symmetry, marginal homogeneity or quasi-symmetry. The associated φ-divergence statistics are distributed asymptotically as chi-squared distributions under the null hypothesis. The new estimators and test statistics contain, as particular cases, the classical estimators and test statistics previously presented in the literature for the cited problems. A simulation study is presented, for the symmetry problem, to choose the best function φ₂ for estimation and the best function φ₁ for testing.     

A note on the mean residual life of a coherent system with a cold standby component

In this paper, we investigate the effect of a cold standby component on the mean residual life (MRL) of a system. When the system fails, a cold standby component is immediately put in operation. We particularly focus on the coherent systems in which, after putting the standby component into operation, the failure of the system is due to the next component failure. For these systems, we define MRL functions and obtain their explicit expressions. Also some stochastic ordering results are provided. Such systems include k-out-of-n systems. Hence, our results extend some results in literature.     

Social network and family business: Uncovering hybrid family firms

What does it mean for a private enterprise in China to be embedded in a family? Our purpose here is twofold: (1) use social network analysis to describe what it means for a firm to be embedded in a family, (2) reveal from the application a new kind of firm, not family, yet akin to family. Armed with data on a large probability sample of private enterprises — a third of which meet ownership and employment criteria of being family businesses — we uncover a category of “hybrid family firms” that look modern in the style of firms that exclude family, but operate socially in ways similar to family firms. Our conclusion from summary statistics on the sample is that there are no differences in average performance level or network advantage for the three categories of businesses: family firms, hybrid family firms, and family-excluded firms. The fact that CEOs of family firms and hybrid family firms more often turn to family as key business contacts is a fact about network composition that raises no question about network mechanisms. Whether the CEO turns to more or fewer family contacts, government help is more likely with stronger political connections, and business success and survival are more likely with a large, open network. That said, the look-modern, act-traditional hybrid family firms stand alone in prospering with a CEO embedded in a closed business network. Recognition of hybrid family firms adds to the literature’s illustrations of social network analysis used to distinguish types of businesses and business people, and extends the population of organizations within which governance and strategy are likely to be better understood when viewed through a family logic.     

Business reform outcomes: Why so different?

Post-crisis policy making increasingly focuses on doing business reforms. We argue that the effects of those reforms will be different across countries. To understand the reasons for the reform outcome divergence, we advance a novel firm-size distribution (FSDs) argument. At the center of the argument is the fact that FSDs are different across countries and stable over time. Then, if a given doing business reform induces firms of different size to grow differently, this will produce a variety of reform outcomes across countries. To advance the argument, we set up a tractable general equilibrium (GE) model and study how firms of different size grow after a doing business reform. The model predicts that larger firms will grow faster than smaller firms after the reform. The model predictions are tested on the Enterprise Surveys (ES) data, merged with the Doing Business indicators. We confirm that firms of different size grow differently after a Doing Business reform. Thus, based on the notable differences of firm size distributions across countries, identical reforms to start, operate and close a business will produce a variety of reform outcomes across countries.